Indefinite Definition and 296 Threads

Homework Statement What is the connection between the Indefinite integral and the Fundalmental theorem of calculus (1st part)? The Attempt at a Solution They are the same to me but the FT is more formal.

I've been wondering how all those indefinite integrals in a comprehensive table were figured out. Can they all be done with one (or some combination) of the standard methods, (substitution, parts etc.)? Or did somebody just poke around until they figured them out? For example, how do you find...

How can I evaluate \int\frac{dx}{\sqrt{1-2x-x^2}} using inverse trig functions? Thanks.

How to evaluate \int{\frac{\arccos{x}}{x^2}\,dx}?

Hi, I need help evaluating the following integral by integration by parts: \int(a^2-x^2)^n\,dx. Specifically I am supposed to prove the following formula: \int(a^2-x^2)^n\,dx=\frac{x(a^2-x^2)^n}{2n+1}+\frac{2a^2n}{2n+1}\int(a^2-x^2)^{n-1}\,dx+C Any hints would be appreciated. Also, does...

how to evaluate the indefinite integral \int \frac{1}{\sqrt{x^2-1}} dx

how to evaluate the indefinite integral ∫(x^2-1)^(-1/2) dx and ∫x^(-1)*(1-x^2)^(-1/2) dx

Homework Statement Integrate: \int \frac{1}{\sin{x}+cos{x}}dx Homework Equations The one above and basic integration formulae which need not be mentioned. The Attempt at a Solution \int \frac{1}{(\sin{x}+cos{x})}...

Don't understand why "an indefinite integral is valid only on a interval" Hi I'm using Stewart's Calculus, in the section of indefinite integral, they say: "Recall from Theorem 4.10.1 that the most general antiderivative on a given interval is obtained by adding a constant to a particular...

1. \int(x^{2} + 5)^{3}dx This is what the book gives as the answer 1/7x^{7} + 3x^{5} + 25x^{3} + 125x + C I got something way different. Where are they getting the 3x^5 and 25x^3 from? Thanks. -v.b.

Homework Statement How is this function continuous from 0 to infinity F(x) = \int\frac{1}{t}dt from x to 2x Homework Equations I am fairly sure that this equation uses the properties of natural logs to solve. Also an infinite function has a derivative that is equal to 0. The...

Homework Statement Hey guys, I'm trying to teach myself how to integrate an indefinite integral. I just am wondering what you can do with something like this: Homework Equations \int 15/(3x+1) dx The Attempt at a Solution I'm trying to figure out how to go backwards, but I...

Helo everyone, can somebody post the best algorithm/strategy to solve indefinite integral questions which are usually asked to undergraduates. The most general set of steps that can be applied to every question one encounters in the classroom. Algo that though may be proved to be inconvenient...

Homework Statement Evaluate the Integrals: \int \frac{-2}{\sqrt{1 - x^2}} dx \int \frac{2x+5}{x^2+6x-3} dx \int \frac{x^3}{x^2-1} dx \int \frac{x}{1+x^4} dxVerify that this integral is correct: \int ue^a^u du = \frac{e^a^u}{a}(u-\frac{1}{a})+C

Hi, here is the question integrate x^3/(x^5-1)

Homework Statement ok I am given this problem indef. int (1+tan^2*5x)dx i need to use the u subsitution method to find the answer but i cannot seem to find what to subsitute the worksheet says the answer is " one-fifth*tan5x+C Homework Equations The Attempt at a Solution

Homework Statement Find the indefinite integral of \int \frac{sec^2 x}{\sqrt{1-tan^2 x}} dx I'm stuck on how to proceed with the denominator. I know that \sqrt{1+tan^2 x} is equivalent to \\sec\theta but I can't seen to find an equivalent to what I have. Can anyone give...

Homework Statement Using improper integrals, find the Laplace transform of f(t)=t, determining the values of s for which the transform is valid.Homework Equations The Laplace transform F(s) of a function f is defined as ∞ / F(s)= | f(t)e^(-st) dt...

Problem: [int]cosx(sinx)dx Given: x=pi; f(pi)=13.4 I am utterly confused on how to solve this integral. I am 99% positive (which is nothing in the math world) that I need to apply the product rule to all of this in order to find the antiderivative. However, no matter how I think of going about...

Homework Statement Integrate (x^3)sqrt(1-x^2) Homework Equations The Attempt at a Solution I used trig. substitution along with u substitution and came up with (x^4)/4 +C which I know is wrong. My professor gave the answer -(((3x^2)+2)((1-x^2)^(3/2)))/15 . Please help!

Homework Statement I want to prove the standard result for indefinite integrals that \int \frac{1}{a^2-x^2} .dx\ =\ \frac{1}{2a}\ln{(\frac{a+x}{a-x})} \\ \mbox{But the problem is that i am unable to do so. I get this--} \int {\frac{1}{a^2-x^2} .dx } \\ = \frac{1}{2a}\int...

There is a simple formula for calculating \frac{df(x)}{dx} u^n where u is a function of x and n is a positive rational number: \frac{df(x)}{dx} u^n = nu^{n-1} \ast \frac{du}{dx} . Is there a similar formula for calculating \int u^n dx where u is a function of x and n is a positive rational...

periods. Like (1+6%/100)^100-1=0.061817441 (1+6%/1000)^1000-1=0.061834635 does it converge to a limit of like 0.06184 or something like that?

I've had this very basic question on the back of my mind for 2 almost years now and I think I've found a satisfactory answer. The question is this most simple one: how do we justify a change of variables such as \int e^{ax}dx = \int \frac{1}{a}e^udu in an indefinite integral? My "solution" is...

evaluate the indefinite integral cos^4(x)sin(x)dx I tried using the half angle formula but this gives me a much more difficult integral, so i resorted to just regular substitution but am not sure if I can do this. u = cos(x) du = -sin(x)dx indefinite integral -u^4du then -1/5(u)^5...

Hey. Say i was given this indefinite integral to evaluate: http://img126.imageshack.us/img126/6374/aaaaog3.gif How could i do that? I can do it by first expanding it all, but that takes a very long time and is quite tedious, especially with such a large index as 7. Is there another way i...

I'm supposed to integrate the following expression, and supposedly there is a very simple way to do so. Maple comes up with something rediculous, so I'd appreciate any input. Sorry about the short hand, don't know how to make everything pretty on here: Integral[(e^ax)cos^2(2bx)dx] where a and...

evaluate the indefinite integral ((e^x)/((e^x)+1))dx I let u = ((e^x)+1) then du = (e^x)dx which occurs in the original equation so.. indefinite ingegral ((u^-1)du) taking the antiderivative I get 1 + C is this right? thanks!

i have a small (i think) question: a value of zero is a definite value, right? it's easily quantifiable. you either have it or you don't. and a value of 1 is also definite. however, a value of infinity is not definite. it's an indefinite value. now, the question is... do quantifiable...

Hi everyone. I'm having some trouble evaluating the following integral \int{sin^4xdx} First let me start off by showing what I did. = \int{(sin^2x)(sin^2x)dx} =\int{[\frac{1}{2}-\frac{1}{2}cos(2x)] \ [\frac{1}{2}-\frac{1}{2}cos(2x)]dx...

I need to integrate this indefinite integral: 1/(x-6)^2 dx Here is my work... Let u= x-6 du/dx=1 so: integral 1/u^2 du = 3/u^3 + c (constant) =3/(x-6)^3 + c Have I gone wrong? And if so where? Thanks

I have: int (1/(sqrt -x^2 -2x))dx so I rewrite (-x^2-2x) --> 1-(x+1)^2 and swap those two. then I say t=x+1, and substitute that in. So now I have: int (1/(sqrt 1-t^2)) dt Here I get stuck, can anyone please help?

Evaluating indefinite integral -- toughie! I have the velocity function v(x) = [(k*x^2)/(2*m)] + v0 I need to integrate this to get position as a function of time. So v = dx/dt. Separating variables, I get t = Integral [2m/(2mv0 + kx^2)] Here's where I'm stuck...If i pull out the 2m, then I...

Calc I - Simple Indefinite Integration Problem Hello, Here is an indefinite integration problem I have been working on. Would anyone be willing to check my solution? Are my assumptions about replacing the C and -C correct? http://img457.imageshack.us/img457/8933/problem0kw.jpg"...

How is this problem integrated? \int \sqrt{ \sin x} \; dx

How do I find the indefinite integral of 1/[(e^x)+(e^-x)] ? Do I have to multiply by [(e^x)-(e^-x)]/[(e^x)-(e^-x)] to eliminate the denominator? !

Well, this is an embarrassingly elementary question, but in my lecture slides (for an electrical engineering course, not a math course) the prof suddenly springs this claim on us: The true definition of an indefinite integral is: \int{f(t)dt} \equiv \int_{-\infty}^{t} {f(\tau) d\tau}...

\!\(∫x^2/Sqrt[1 - x^2] \[DifferentialD]x\) I need to find the integral of (x^2)/ Sqrt(1-(x^2)) if the above doesn't work properly integration by parts results in 0=0 how do i do this?

I am just curious I was thinking about this and if anyone could explain I would appreciate it. I am curious to know how to find the indefinite integral of xsinx with respect to x. Thanks, David

\int sin(9x)sin(16x)dx is there another way of solving the problem above besides using the multiple angles formula?

Hello all If you have the funtions: y = x^2, y = sin x, y = 2x^4 and you are asked to set up the corresponding integrations, would it be: \int^b_a 2u du = x^3 \int^b_a -\cos u du = \sin x \int^b_a 8u^3 du = 2x^4 Thanks

Hi there, Can someone explain to me what the following are and how each one is used as a tool for the next one: 1)Indefinite integral 2)Riemann Sum 3)Definite Integral 4)Fundamental Theorem of Calculus(The part which says that the derivative of the integral of f(t)dt from a to x is...

Ok. Im' confused between the difference of definite and indefinite integrals. \int\limits_a_b \int The first integral here which is \int\limits_a_b is about area below a curve. Where a and b is the difference of the area under the function f(x). The \int\ is just the...

I've been trying to integrate the following function but have gotten somewhat stuck doing it. The answer i managed to produce gave some bogan answers. the integral in question is \int e^\frac{-(x-\mu)^2}{(2\sigma)^2} where \mu and \sigma are constants. its part of the normal...

When they ask you to set up integral formulas for the derivative of 1/(x+1), would you use the fundamental theorem of calculus and set up a definite integral, or an indefinite integral. Can someone help me clarify this? Thanks

Hi! I am stuck with this integration problem: Thanks in advance.